Ratios of consecutive values of the divisor function
Number Theory
2025-10-31 v2
Abstract
We show that the sequence of ratios of consecutive values of the divisor function attains every positive rational infinitely many times. This confirms a prediction of Erd\H{o}s.
Cite
@article{arxiv.2505.00727,
title = {Ratios of consecutive values of the divisor function},
author = {Sean Eberhard},
journal= {arXiv preprint arXiv:2505.00727},
year = {2025}
}
Comments
3 pp. Accepted version. To appear in the Journal of Number Theory